Jayashree Thota wrote:In the figure to the right, if point C is the center of the circle and DB = 7, what is the length of DE in triangle EDB?



(1) x = 60°

(2) DE || CA

Given: Point C is the center of the circle and DB = 7;
Question: What is the length of DE in triangle EDB?

Let's take each statement one by one.

(1) x = 60°

In ∆ABC, AC and BC are radii, thus the angles opposite them must be equal. Thus, /_ABC = /_BCA = xº = 60º. This means that /_ CAB = 180 - 60 - 60 = 60º. So, ∆ABC is an equilateral traingle.

However, the relationship between ∆ABC and ∆BDE is not established. Thus, we cannot get the value of DE. Insufficient.

(2) DE || CA

Again, in ∆ABC, AC and BC are radii, thus the angles opposite them must be equal. Thus, ∆ABC is an equilateral triangle.

Let's observe ∆ABC and ∆BDE under the light of DE || CA

/_BCA = /_BDE
/_BCA = /_BED
/_ABC is a common angle for both the traingles.

Thus, ∆ABC and ∆BDE are similar triangles.

Using the property of similar triangles, we have

BC/BD = AC/DE

3.5/7 = 3.5/DE

=> DE = 7. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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